time expectations for sights in Warsaw

I found the Royal Castle a bit underwhelming - may have spent just an hour or a little more there. It may be enough to visit the square outside and walk around the area.

Would allow between two and three hours for the Uprising museum if you find the subject matter interesting. Be sure to watch the seven minute animated flyover film showing the city as the Germans left it at the end of the war, as it will give you an appreciation for the city as it exists today. It's in a small screening room off on one side and you should expect to wait in line for it.

While you're in that area, the food hall that's a few blocks away is a worthwhile stop for lunch.

I made multiple trips to both the Warsaw Rising Museum and the Museum of the History of Polish Jews. The total time spent in each one was probably close to 8 hours, but I am someone who reads every word posted in English in such places and also watches any English-accessible videos.

I think the Cold War Museum had a different name when I saw it in 2018. At that time it had a relatively narrow focus--the story of the Polish military officer who spied for the CIA and whose story is told in the (interesting) movie, "Jack Strong". It is (or was) quite a small museum, where I probably spent between 1 and 2 hours (and, again, I read everything). I just stumbled on the museum while I was walking around the Old Town, and it seemed as if it might have just opened. It was quite interesting, but if your time is tight, you might watch the movie before your trip and skip this. That said, I can't tell from the museum's website whether the exhibits have been significantly expanded; it may have been a work in progress back in 2018.

I went to the Royal Castle, which per Wikipedia is basically an art museum. I go to every art museum I run into and have no idea how long I spent at this one. I remember also liking the National Museum and several others in the city.

I didn't go to the Polish History Museum. It opened in 2018, the year I visited Poland, and I'm not sure it was even open when I was in the city.

I also did not go to the Museum of Warsaw.

The city has quite a number of other very good museums, several of them related to WWII. I was very impressed with the quality of the museums in Warsaw--and elsewhere in Poland--and very much appreciated how well the historical museums in particular catered to English-speaking visitors.

how long to plan a visit at these sites ...

With any tourist site you have personal interest in just go and leave when you feel like you've seen enough, and don't count on going to all of them; everyone has different interests; a tourist site will not appeal to everyone equally the same.